There are several ways of addressing this challenge and I employ two methods in my kiln, depending on where the pots are to be placed. The first is to try to prevent the pots from sticking. My first step in this process is to design my feet so that there is a minimum amount of surface area in contact with the kiln shelf. The foot ring itself is trimmed with a chamfer on each edge so that only a thinly angled line touches the shelf. This also creates a slight overhang to help prevent fly ash from getting under the foot. When the vessel is removed from the kiln the foot ring can be touched up with some sand paper and "Viola!", a nice smooth foot ring. When I am waxing the feet of some vessels before glazing, on plates for example, I use a special wax mixture of candle wax, kerosene and a handful of alumina powder. The wax burns off in the kiln, leaving a very fine residue of alumina between the vessel and the kiln shelf. Alumina (Al2O3) is a highly refractory material, the melting point of which is about 2040C, and so it remains as a dry powder even at glaze firing temperatures, and will serve the same purpose as flour on the work bench when you are making pastry or bread, preventing sticking. Following the same train of thought, Alumina is used as a coating on kiln shelves and kiln furniture to prevent sticking, just as flour is used on the inside of a cake tin. On its own, however, alumina floats around as a powder and can stick to glaze surfaces making them matte and unattractive, so a coating mixture containing some clay material as a fixative is necessary. The mixture which I use is Alumina 2: Kaolin 1 proportionately by weight, mixed with enough water to make is a pourable creamy consistency. I put this into a watering can and pour it over the surface of the kiln shelves, then put them out in the sun to dry. After every firing I scrape any accumulated ash or soda deposits off the kiln shelves, so that they are ready to be coated again for the next firing. It is important to use a dust mask and eye protection during this process! The materials are all non toxic, but inhaling dust can cause lung disease, and chips of broken glass in the eyes should be avoided at all costs!
My other approach to this challenge is to accept that a wood or soda firing is what it is. There is going to be ash and glass dripping of the pots, and it's going to leave marks. If you are trying to avoid that and it happens by accident it can leave nasty scars on the pots. If, however, you accept it and allow it to happen as a part of the total design, those marks become cicatrices, like tribal scars, and a beautiful expression of the firing process in the finished work.
I do not use wad mix directly on the clay, as that goes in the nasty scar basket. Instead I use a ball of fire clay, rolled in alumina, stuffed inside a sea shell. A set of three, or sometimes more, of these will form a stand on which the vessel can be placed, raising it off the kiln shelf. When the kiln is fired, the salt in the shell will volatilize off leaving flashing marks on the clay. The Calcium Carbonate (CaCO3) in the shell will lose Carbon Dioxide (CO2) and become Calcium Oxide (CaO), still retaining its original structure between the vessel and the fire clay. Any glaze, ash or soda will flow into the shell structure. When the vessel is removed from the kiln and placed in a bucket of water, the Calcium Oxide (Quick lime) will rehydrate to become Calcium Hydroxide (Ca(OH)2 or Slaked Lime), and will just wash off the vessel leaving a fossil like cicatrix where it was in contact with the surface. The slaked lime goes on the compost heap. A touch up of the sharp edges left on the glaze deposit with some sand paper, and Robert is your fathers brother! This is the method I use at the fire face, where the forces of nature are most energetic and capricious. I described this process and my feelings about it in my "Art for Eternity" entry, and I invite you to read that by all means. The greatest challenge for a potter, however, is knowing when to take control, and knowing when to surrender it. It is this balance, this dance with the elements, that creates such beauty, that gives great joy to the user of these vessels, and makes being a potter such a fulfilling career.